Introduction to spectral methods
نویسنده
چکیده
This proceeding is intended to be a first introduction to spectral methods. It is written around some simple problems that are solved explicitly and in details and that aim at demonstrating the power of those methods. The mathematical foundation of the spectral approximation is first introduced, based on the Gauss quadratures. The two usual basis of Legendre and Chebyshev polynomials are then presented. The next section is devoted to one dimensional equation solvers using only one domain. Three different methods are described. Techniques using several domains are shown in the last section of this paper and their various merits discussed.
منابع مشابه
Prediction of the response to repetitive transcranial magnetic stimulation by spectral powers of prefrontal regions of brain.
Introduction: Quantitative assessments of the effects induced by repetitive transcranial magnetic stimulation (rTMS) are crucial to develop more efficient and personalized treatments. Objectives: To determine the spectral powers of different subbands of EEG correlated with treatment response to rTMS. Materials and Methods: the spectral powers of different...
متن کاملAn Overview of Nonlinear Spectral Unmixing Methods in the Processing of Hyperspectral Data
The hyperspectral imagery provides images in hundreds of spectral bands within different wavelength regions. This technology has increasingly applied in different fields of earth sciences, such as minerals exploration, environmental monitoring, agriculture, urban science, and planetary remote sensing. However, despite the ability of these data to detect surface features, the measured spectrum i...
متن کاملA New Dictionary Construction Method in Sparse Representation Techniques for Target Detection in Hyperspectral Imagery
Hyperspectral data in Remote Sensing which have been gathered with efficient spectral resolution (about 10 nanometer) contain a plethora of spectral bands (roughly 200 bands). Since precious information about the spectral features of target materials can be extracted from these data, they have been used exclusively in hyperspectral target detection. One of the problem associated with the detect...
متن کاملCommon Raman Spectral Markers among Different Tissues for Cancer Detection
Introduction Raman spectroscopy is a vibrational spectroscopic technique, based on inelastic scattering of monochromatic light. This technique can provide valuable information about biomolecular changes, associated with neoplastic transformation. The purpose of this study was to find Raman spectral markers for distinguishing normal samples from cancerous ones in different tissues. Materials and...
متن کاملTarget Detection Improvements in Hyperspectral Images by Adjusting Band Weights and Identifying end-members in Feature Space Clusters
Spectral target detection could be regarded as one of the strategic applications of hyperspectral data analysis. The presence of targets in an area smaller than a pixel’s ground coverage has led to the development of spectral un-mixing methods to detect these types of targets. Usually, in the spectral un-mixing algorithms, the similar weights have been assumed for spectral bands. Howe...
متن کاملChebyshev Spectral Collocation Method for Computing Numerical Solution of Telegraph Equation
In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...
متن کامل